Answer:
Yes, the height of the tree is a function of the number of months. A function is a relation where each input (independent variable) is associated with exactly one output (dependent variable). In this case, the number of months is the input, and the height of the tree is the output.
Now, let's determine if the function is linear or nonlinear. A linear function is a function where the output (dependent variable) changes at a constant rate for each unit change in the input (independent variable). In other words, the graph of a linear function forms a straight line.
In this scenario, the height of the tree increases by one foot each month. Since the height of the tree increases at a constant rate (one foot per month), the function is linear. The relationship between the number of months and the height of the tree can be expressed as:
Height = 5 + Number of months * 1
The "5" represents the initial height of the tree, and the "Number of months * 1" represents the additional height gained each month. As it forms a straight line when graphed, it confirms that it is a linear function.